Personal computers linked by the Internet just wouldn’t have been practical until the “processer on a chip” fourth generation of computers were available. The best mainframe computers of the 1960s would have had trouble playing Pong, much less handling megabytes of data. You could have advanced the Internet by about twenty years, but the hardware just wasn’t available earlier.
Still, I can see that in another world computing could have been around for much longer. The Babbage engine is a good takeoff point for an alternate history. In real life Babbage spent years trying to create parts machined closely enough to build his difference engine. Let’s suppose that instead, he’d simply publicly offered a large reward to anyone who could build parts to the necessary tolerances, and some unsung mechanic solved the problem for him. Say a full-scale Analytical Engine becomes available by the 1840s. The timeline I see goes like this:
1840 Analytical Engine built. Dramatically improves standardized tables of logarithms, trig functions, and naval emphemeris tables.
1875 First electro-mechanical computer built using telegraph technology.
1880 First demonstration of networking using two computers linked by telegraph.
1890 First mathematical analysis of computability devised. Speculations about whether a machine could be intelligent.
1895 H. G. Wells writes a science-fiction story about an intelligent computer; Sir Conan Doyle writes a Sherlock Holmes story featuring a gambler who uses a computer connected to a telegraph line to beat the odds at a casino.
1915 Computers widely used during the Great War to calculate artillery tables. German U-boats equipped with cypher machines. British mathematical group uses computers to break codes.
1923 First all-electronic vacuum tube computer built.
1927 First permanently networked computers using dedicated telegraph lines.
1928 Computerized stock quotes used with ticker-tape machines.
1930 First computer-controlled direct dial telephone system in New York City.
1931 First higher-level programming language devised, using electric keyboard and teletype feedback.
1932 Western Union offers first national credit-card system. Initially limited to businesses catering to the wealthy.
1932 Election of Roosevelt as President predicted by computer.
1933 Magnetic media storage of computer programs and data
1934 Commercial computers linked by telephone modems.
1935 Cathode-ray tube first used as computer monitor.
1936 New Deal project establishes nation-wide long distance telephone service.
1937 Popular Mechanics publishes plans for build-it yourself vacuum tube home computer.
1938 Woolworth’s becomes first national department store chain to offer credit-card purchasing.
1939 World’s Fair features computer-controlled Home of the Future.
1939 Computerized population database established by Nazi Germany to further eugenics goals.
1940 Computers used to create military defense net coordinating British radar/ air defense system.
1941-1944 Computers used extensively by Manhatten Project for physics calculations. Prototype of packet-based data system used to pass encrypted data between Oak Ridge, Hanford and Los Alamos. Reactor and bomb designs advanced by ten months. Trinity test carried out September 1944.
1946 Hobbyists establish Bulletin Board Systems for home computers linked by modems.
1949 Defense Department orders construction of computerized peer-to-peer nuclear war command network.
1950 Western Union creates national commercial data packet service allowing any two subscribing computers to send messages to each other.
1951 Revelations that Soviet spies used “Trojan Horse” programs to steal data from Manhatten Project. Computer and network security concerns raised.
1952 First transistorized computers marketed.
1953 Device for outputting computer text to TV screen available by order from electronics shops.
1954 First complete home computer marketed by General Electric as a way of automating home appliances. Fails to catch on with consumers but adopted by hobbyists for BBS-ing and for amatuer written text-based games.
1957 Following launch of Sputnik, calls for major revision of America’s schools include proposal that all high school students learn computer programming.
1958 First integrated-circuit computers built.
1960 First simple video games- “Pong”, etc.